11. Solve the following linear program using the graphical solution procedure:
Max 5A + 5B
1A < 100 (Less than or equal to is the sign)
1B < 80 (Less than or equal to is the sign)
2A + 4B < 400 (Less than or equal to is the sign)
A , B > 0 (Greater than or equal to is the sign)

Production Time (hours)
Cutting Inspection Profit
and and per
Product Dying Sewing Finishing Packaging Bag
Standard 7/10 1/2 1 1/10 $10
Deluxe 1 5/6 2/3 1/4 $9

15. Suppose that Par's management (Problem 14) encounters the following situation:
a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.
B. A new lost-cost material is available for the standard bag, and the profit contribution per standard bag can increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.)
c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A + 9B is the appropriate objective function.)
If each of these situations is encountered separtely, what is the optimal solution and the total profit contribution?

23. Embassy Motorcycles (EM) manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced.
a. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit.
b. Solve the problem graphically. What is the optimal solution?
c. Which constraints are binding?

Production Time (hours)
Cutting Packaging 
Model and Sewing Finishing and Shipping Profit/Glove
Regular model 1 1/2 1/8 $5
Catcher's model 3/2 1/3 1/4 $8

25. George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond form. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%.
a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.
b. Solve the problem using the graphical solution procedure.

Standard Grade Professional Grade
Fiberglass 84% 58%
Carbon fiber 10% 30%
Kevlar 6% 12%

39. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis's risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is riskier investment. Innis's client also specifies that at least $300,000 be invested in the money market fund.
a. Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.
b. How much annual income will this investment strategy generate?
c. Suppose the client desires to maximize annual return. How should the funds be invested?